8.5 Numerical and Analytical Results for a Rectangular Cross-Sectional Beam Resonator 327
Fig. 8.11 Beam with boundary conditions (s − s) for F = 0.260417: a dependence of ω 2
N L on
vibration amplitude w; b quality factor Q N L versus beam vibration amplitude w
Fig. 8.12 Comparison of the eigenfrequencies for the (s − s) beam: a F = 0; b F = 0.260417
the linear vibration mode (8.105). Figure 8.10a presents the dependence of nonlinear
frequencies ω
2
N L obtained via formula (8.104) versus the vibration amplitude w, and
in Fig. 8.10b the quality factor Q N L of the beam resonator with the lack of the size
dependence (F = 0) is given for three values of the beam length.
Analogous results for F = 0.260417 are presented in Fig. 8.11.
In order to check the reliability of computation of eigenfrequencies, the obtained
analytical results have been compared with numerical solutions.
Figure 8.12 presents the results of comparison for the beam (s − s) for F = 0
(a) and for F = 0.260417 (b), i.e. taking into account the size-dependent behaviour
obtained numerically (8.2) and analytically (8.1).
Figure 8.13 presents the results of comparison of the eigenfrequencies computed
for the (s − s) beam for F = 0 (a) (without the size-dependent behaviour) and for
F = 0.260417 (b) with the size-dependent behaviour.